Trigonometry Examples

Simplify (3(cos(48)+isin(48)))^5
Step 1
Apply the distributive property.
Step 2
Use the Binomial Theorem.
Step 3
Simplify terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Apply the product rule to .
Step 3.1.2
Raise to the power of .
Step 3.1.3
Apply the product rule to .
Step 3.1.4
Multiply by by adding the exponents.
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Step 3.1.4.1
Move .
Step 3.1.4.2
Multiply by .
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Step 3.1.4.2.1
Raise to the power of .
Step 3.1.4.2.2
Use the power rule to combine exponents.
Step 3.1.4.3
Add and .
Step 3.1.5
Raise to the power of .
Step 3.1.6
Multiply by .
Step 3.1.7
Apply the product rule to .
Step 3.1.8
Raise to the power of .
Step 3.1.9
Multiply by .
Step 3.1.10
Use the power rule to distribute the exponent.
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Step 3.1.10.1
Apply the product rule to .
Step 3.1.10.2
Apply the product rule to .
Step 3.1.11
Raise to the power of .
Step 3.1.12
Rewrite as .
Step 3.1.13
Multiply by .
Step 3.1.14
Multiply by .
Step 3.1.15
Apply the product rule to .
Step 3.1.16
Raise to the power of .
Step 3.1.17
Multiply by .
Step 3.1.18
Use the power rule to distribute the exponent.
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Step 3.1.18.1
Apply the product rule to .
Step 3.1.18.2
Apply the product rule to .
Step 3.1.19
Raise to the power of .
Step 3.1.20
Factor out .
Step 3.1.21
Rewrite as .
Step 3.1.22
Rewrite as .
Step 3.1.23
Multiply by .
Step 3.1.24
Multiply by .
Step 3.1.25
Multiply by .
Step 3.1.26
Use the power rule to distribute the exponent.
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Step 3.1.26.1
Apply the product rule to .
Step 3.1.26.2
Apply the product rule to .
Step 3.1.27
Raise to the power of .
Step 3.1.28
Rewrite as .
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Step 3.1.28.1
Rewrite as .
Step 3.1.28.2
Rewrite as .
Step 3.1.28.3
Raise to the power of .
Step 3.1.29
Multiply by .
Step 3.1.30
Multiply by .
Step 3.1.31
Use the power rule to distribute the exponent.
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Step 3.1.31.1
Apply the product rule to .
Step 3.1.31.2
Apply the product rule to .
Step 3.1.32
Raise to the power of .
Step 3.1.33
Factor out .
Step 3.1.34
Rewrite as .
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Step 3.1.34.1
Rewrite as .
Step 3.1.34.2
Rewrite as .
Step 3.1.34.3
Raise to the power of .
Step 3.1.35
Multiply by .
Step 3.2
Simplify the expression.
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Step 3.2.1
Reorder factors in .
Step 3.2.2
Reorder and .
Step 3.2.3
Reorder and .